Molar Fractions, fucking chemistry

Okay, so an element Q exists in two states, 320Q and 319Q. It's overall atomic mass is 319.58 as it appears on a hypothetical periodic table. 319Q's atomic mass is 319.02 g/mol and 320Q's atomic mass is 320.04 g/mol. The 319.58 is composed of the average amount of the two per mol of Q. What are the molar fractions of 320Q and 319Q respectively?

Me and my friend have been trying to figure this out and he says it's done like this:

%320Q=320.04/(319.02+320.04) to get .5007980471 (5008%)

I say that's bullshit because by just plug 'n checking I get that Q320 should be closer to 55%

How is this type of problem done?

Oops.

I meant, "exists as two isotopes."

I just did some math on it; I don't know if there is a standard method.  (I don't even know the term "molar fractions".)  For 319.02 and 320.04 to average to 319.58, the 319.02 has to be weighted at about 52.94%, and the 420.04 has to be weighted at about 100% - 52.94% = 47.06%.

typo, replace 420.04 with 320.04

I have food stuck in my molars...

Thanks, but is there a specific way to get to those numbers? i.e. is there a method other than just guessing and trying to get close?

A molar fraction (noted xi) is what % of a given substance is in a mole of your compound (for example if element Q is one-third Q319 and two-thirds Q320 their respective molar fractions are .33 and .66)

From the problem we can write two equations
a) x + y = 1
where x is the molar fraction of Q319 and y the molar fraction of Q320. there are only two substances so their sum must equal 100% (1)

b)319.02*x + 320.04*y = 319.58*1
this is a similar equation but each term has been multiplied by its respective molar mass (noted Mi) I'm probably not explaining this enough but look up in your manual: moles, molar mass, molar fraction. M1 * x1 + M2 * x2 = M3 * (x1+x2)

replace x by 1-y, isolate y
y = 0,549 = 54.9%
x is the remainder (1-0.549) = 0,451 = 45.1%

45.1% Q319, 54.9% Q320

Without banging my head too much what your friend did is probably incorrect because it doesn't take into account the overall molar mass of the substance

I think the answer is 37.652 but I'm not sure how I got it

Well the weight would be m1 if it were 100% 320 and m2 if it were 100% 319.

So just make a graph of weight vs percent composition and draw a line between the two points and TI-83 your way to success.

>>7
[quote]we[/quote]

You are not a textbook.

[q]we[/q]

fucking shit how do you make a motherfucking quote on this motherfucking board?

fucking shit how do you make a motherfucking quote on this motherfucking board?

Like this.

>>12

hi

>>7

Thanks! I went to an open physics/chemistry tutor on campus and he showed me like this:

319.58=(x1*319.02)+(x2*320.04)

I understand that x1 + x2 must equal 1 (100%)

So x1 must be equal to 1-x2 and x2 must equal 1-x1

319.58 = (1-x2)319.02+ x2*320.04

Distribute (1-x2)319.02

319.58=319.02+(x2*320.04)-(x2*319.02)
319.58=319.02+x2(320.04-319.02)
319.58-319.02=x2(1.02)
.56=x2(1.02)
x2=.56/1.02=.549
320Q=54.9%
319Q=45.1%